Information on the high-pressure rheological properties of methane hydrate sediment slurry is an important precursor to understanding their impact on the mechanical behavior of host sediments during natural gas production from hydrate reservoirs. However, rheological analysis of gas hydrate slurries in the presence of natural sediments containing complex minerals and salts is not yet available in the open literature. The multiphase nature of hydrate system is another challenge when it comes to the high-pressure rheological study. Because the conventional Couette geometry does not ensure proper mixing of solid, liquid, and gas phases during hydrate formation and rheological measurements in a multiphase system, in this work, it has been modified to enhance the mixing capabilities. In this work, the rheological experiments on methane hydrate formation in sediment sample collected from the Krishna-Godavari Basin of offshore India have been performed. Rheological investigations were carried out using three different sediment concentrations of 10, 35, and 50 wt %, each at varying hydrate formation temperatures and pressures of 273.15, 275.15, 283.15, and 285.15 K and 10 MPa, respectively. Viscosity profiles of the methane hydrate sediment slurry containing three sediment concentrations at each temperature were analyzed for varying shear rates during hydrate formation. Also, rheological studies have been performed on methane hydrate sediment slurry during hydrate dissociation using thermal stimulation. Experimental case studies were conducted to understand the effect of varying hydrate, sediment, and water volume content in the slurry on the viscosity profile. The work is an endeavor to explain the underlying causes of the rheological behavior of hydrate slurries in marine sediments.